I think for a lot of those kinds of people it's pathological. For example, I remember reading in Careless People (a memoir by a former Facebook/Meta employee) about some of the things the author witnessed about Mark Zuckerberg made it seem like he only wanted to do things because no one else could, not because he personally derived any enjoyment out of it. I've seen this personally with philanthropists too. They don't actually like the disadvantaged kids they're helping (I'm talking literal racists), but they like the idea that they're the only ones that these kids can turn to. Basically I'm saying I don't think they believe life is zero-sum, but they have a pathological need to create zero-sum circumstances where they are the "winners" and the rest of us losers.

They believe everything is zero-sum

Well, they're right about that. The Earth, and all the resources on it, are finite. The more any one person owns, the less everyone else can own. Now, I would agree that the Earth's resources are abundant, and that there's more than enough for everyone on Earth (at our current population level, at least) to not only survive but thrive. But, because the Earth's resources are finite, it's not possible for any one person to own an infinite amount of resources, let alone for that person to own infinite resources and there still be resources leftover for everyone else.